Subgroups — #25002595

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582927	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#19134312	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582660	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582660	C₂	1	1	yes	maximal, characteristic
6	#19134293	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×#341	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×#13063284	C₂²	1	1	yes	characteristic
10	C₂×#13063284	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	#14582927	—	2	2	no	—
13	#14582927	C₄	1	4	yes	complemented
14	C₂×Dic₄₃⋊C₈	—	2	2	no	—
15	C₂×C₈×Dic₄₃	—	2	2	no	—
16	C₂×C₈×Dic₄₃	—	2	2	no	—
17	C₂×C₈×Dic₄₃	—	2	2	no	—
18	#14582662	C₄	1	4	yes	complemented
19	#14582660	—	2	2	no	—
20	#14582660	C₄	1	4	yes	complemented
21	#14582653	—	2	2	no	—
22	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#341	—	2	2	no	—
26	C₂³×Dic₄₃	—	2	1	no	—
27	C₂²×C₄₃⋊C₈	—	2	1	no	—
28	C₂²×C₄₃⋊C₈	—	2	1	no	—
29	C₂²×C₄₃⋊C₈	—	2	1	no	—
30	C₂²×C₄₃⋊C₈	—	2	1	no	—
31	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
32	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
33	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
34	#13063284	—	2	1	no	—
35	#13063284	—	2	1	no	—
36	#13063284	—	2	1	no	—
37	#13063284	—	2	1	no	—
38	#13063284	—	2	1	no	—
39	#13063284	—	2	1	no	—
40	#13063284	C₂×C₄	1	2	yes	—
41	#13063284	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
44	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
45	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
46	C₂×C₄×Dic₄₃	—	2	1	no	—
47	C₂×C₄×Dic₄₃	—	2	1	no	—
48	C₂×C₄×Dic₄₃	—	2	1	no	—
49	C₂×C₄×Dic₄₃	—	2	1	no	—
50	C₂×C₄×Dic₄₃	—	2	1	no	—
51	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
53	C₂×C₄×Dic₄₃	Q₈	1	2	yes	—
54	Dic₄₃⋊C₈	—	2	8	no	—
55	C₈×Dic₄₃	—	2	8	no	—
56	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₄₃	—	2	1	no	—
58	C₂×M₁₆×C₄₃	—	2	1	no	—
59	C₂×M₁₆×C₄₃	—	2	1	no	—
60	C₂×M₁₆×C₄₃	—	2	1	no	—
61	C₂×M₁₆×C₄₃	—	2	1	no	—
62	C₂×M₁₆×C₄₃	—	2	1	no	—
63	C₂×M₁₆×C₄₃	—	2	1	no	—
64	C₂×M₁₆×C₄₃	—	2	1	no	—
65	C₂×M₁₆×C₄₃	—	2	1	no	—
66	C₂×M₁₆×C₄₃	—	2	1	no	—
67	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
68	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₄₃	—	2	1	no	—
70	C₂²×C₈×C₄₃	—	2	1	no	—
71	C₂²×C₈×C₄₃	—	2	1	no	—
72	C₂²×C₈×C₄₃	—	2	1	no	—
73	C₂²×C₈×C₄₃	—	2	1	no	—
74	C₂²×C₈×C₄₃	—	2	1	no	—
75	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
76	C₂²×C₈×C₄₃	D₄	1	2	yes	—
77	C₂²×C₈×C₄₃	Q₈	1	2	yes	—
78	C₂⁴×C₄₃	#41	1	1	yes	characteristic
79	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
93	C₂²×Dic₄₃	—	2	8	no	—
94	C₂²×Dic₄₃	—	2	2	no	—
95	C₂²×Dic₄₃	—	2	2	no	—
96	C₂²×Dic₄₃	—	2	2	no	—
97	C₂²×Dic₄₃	—	2	2	no	—
98	C₂²×Dic₄₃	—	2	2	no	—
99	M₁₆×C₄₃	—	2	2	no	—
100	M₁₆×C₄₃	—	2	2	no	—
101	M₁₆×C₄₃	—	2	2	no	—
102	M₁₆×C₄₃	—	2	2	no	—
103	M₁₆×C₄₃	—	4	1	no	—
104	M₁₆×C₄₃	—	4	1	no	—
105	M₁₆×C₄₃	—	4	1	no	—
106	M₁₆×C₄₃	—	4	1	no	—
107	C₂×C₈×C₄₃	—	2	2	no	—
108	C₂×C₈×C₄₃	—	2	2	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	4	1	no	—
116	C₂×C₈×C₄₃	—	4	1	no	—
117	C₂×C₈×C₄₃	—	4	1	no	—
118	C₂×C₈×C₄₃	—	4	1	no	—
119	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
120	C₂²⋊Dic₄₃	—	2	2	no	—
121	C₂²⋊Dic₄₃	—	2	2	no	—
122	C₂²⋊Dic₄₃	—	4	1	no	—
123	C₂²⋊Dic₄₃	—	4	1	no	—
124	C₄⋊Dic₄₃	—	2	2	no	—
125	C₄⋊Dic₄₃	—	2	2	no	—
126	C₄⋊Dic₄₃	—	2	2	no	—
127	C₄⋊Dic₄₃	C₄²	1	4	yes	—
128	C₄×Dic₄₃	—	2	2	no	—
129	C₄×Dic₄₃	—	2	2	no	—
130	C₄×Dic₄₃	—	2	2	no	—
131	C₄×Dic₄₃	—	2	2	no	—
132	C₄×Dic₄₃	—	2	2	no	—
133	C₄×Dic₄₃	—	4	1	no	—
134	C₄×Dic₄₃	—	4	1	no	—
135	C₄×Dic₄₃	C₄⋊C₄	1	4	yes	—
136	C₂×C₄₃⋊C₈	—	2	2	no	—
137	C₂×C₄₃⋊C₈	—	2	2	no	—
138	C₂×C₄₃⋊C₈	—	2	2	no	—
139	C₂×C₄₃⋊C₈	—	2	2	no	—
140	C₂×C₄₃⋊C₈	—	2	2	no	—
141	C₂×C₄₃⋊C₈	—	2	2	no	—
142	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	4	yes	—
143	C₂³×C₄₃	—	2	4	no	—
144	C₂³×C₄₃	#117	1	1	yes	characteristic
145	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
146	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
147	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂³×C₄₃	#123	1	1	yes	characteristic
149	C₂³×C₄₃	#125	1	1	yes	characteristic
150	C₂³×C₄₃	#126	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
156	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
167	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
168	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
169	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
174	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
175	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
176	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
179	C₂×Dic₄₃	—	2	8	no	—
180	C₂×Dic₄₃	—	2	8	no	—
181	C₂×Dic₄₃	—	2	8	no	—
182	C₂×Dic₄₃	—	2	4	no	—
183	C₂×Dic₄₃	—	2	4	no	—
184	C₂×Dic₄₃	—	4	4	no	—
185	C₂×Dic₄₃	—	4	2	no	—
186	C₂×Dic₄₃	—	4	4	no	—
187	C₈×C₄₃	—	2	4	no	—
188	C₈×C₄₃	—	4	2	no	—
189	C₈×C₄₃	—	4	2	no	—
190	C₄₃⋊C₈	—	2	4	no	—
191	#10882	—	43	1	no	maximal, Sylow
192	C₂²×C₄₃	—	2	2	no	—
193	C₂²×C₄₃	—	2	2	no	—
194	C₂²×C₄₃	—	2	2	no	—
195	C₂²×C₄₃	—	2	2	no	—
196	C₂²×C₄₃	—	2	2	no	—
197	C₂²×C₄₃	—	2	2	no	—
198	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₄₃	#385	1	1	yes	characteristic
200	C₂²×C₄₃	#387	1	1	yes	characteristic
201	C₂²×C₄₃	#387	1	1	yes	characteristic
202	C₂²×C₄₃	#387	1	1	yes	characteristic
203	C₂²×C₄₃	#388	1	1	yes	characteristic
204	C₂²×C₄₃	#389	1	1	yes	characteristic
205	C₂²×C₄₃	#443	1	4	yes	—
206	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
207	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
208	C₄×C₄₃	#385	1	1	yes	characteristic
209	C₄×C₄₃	#386	1	1	yes	characteristic
210	C₄×C₄₃	#387	1	1	yes	characteristic
211	C₄×C₄₃	#388	1	1	yes	characteristic
212	C₄×C₄₃	#389	1	1	yes	characteristic
213	C₄×C₄₃	#391	1	1	yes	characteristic
214	Dic₄₃	—	2	8	no	—
215	Dic₄₃	—	4	4	no	—
216	Dic₄₃	—	8	2	no	—
217	C₂×#424	—	43	1	no	—
218	C₂²×C₄×C₈	—	43	1	no	—
219	C₂×#341	D₄₃	1	1	yes	characteristic
220	#1735	—	43	1	no	—
221	C₂×#339	—	43	1	no	—
222	C₂×#339	—	43	1	no	—
223	#1729	—	43	1	no	—
224	C₂×C₄₃	—	2	1	no	—
225	C₂×C₄₃	—	2	1	no	—
226	C₂×C₄₃	—	2	1	no	—
227	C₂×C₄₃	—	2	1	no	—
228	C₂×C₄₃	#1436	1	1	yes	characteristic
229	C₂×C₄₃	#1764	1	2	yes	—
230	C₂×C₄₃	#1937	1	2	yes	—
231	C₂×C₄₃	#1945	1	2	yes	—
232	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
233	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
234	C₂³×C₈	—	43	1	no	—
235	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
236	C₂×#117	—	43	1	no	—
237	C₂×#117	—	43	1	no	—
238	C₂²×C₄²	—	43	1	no	—
239	#424	—	43	4	no	—
240	#424	—	86	2	no	—
241	C₂×C₄⋊C₈	—	86	2	no	—
242	C₂×C₄×C₈	—	86	2	no	—
243	C₂×C₄×C₈	—	86	2	no	—
244	C₂×C₄×C₈	—	86	2	no	—
245	#341	—	2	2	no	—
246	#340	—	43	4	no	—
247	#339	—	43	4	no	—
248	#339	—	86	2	no	—
249	#336	—	86	2	no	—
250	C₄₃	#10882	1	1	yes	characteristic, complemented, Sylow
251	C₂³×C₄	—	86	1	no	—
252	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
264	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	43	2	no	—
272	C₂²×C₈	—	43	2	no	—
273	C₂²×C₈	—	43	2	no	—
274	C₂²×C₈	—	86	1	no	—
275	C₂²×C₈	—	86	1	no	—
276	C₂²×C₈	—	86	1	no	—
277	C₂²×C₈	—	86	1	no	—
278	C₂²×C₈	Dic₈₆	1	2	yes	—
279	C₂²×C₈	C₄×D₄₃	1	2	yes	—
280	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
281	#117	—	43	2	no	—
282	#117	—	43	2	no	—
283	#117	—	86	1	no	—
284	#117	—	86	1	no	—
285	#117	—	86	1	no	—
286	#117	—	86	1	no	—
287	#117	—	86	1	no	—
288	#117	—	86	1	no	—
289	C₂×C₄⋊C₄	—	43	2	no	—
290	C₂×C₄⋊C₄	—	43	2	no	—
291	C₂×C₂²⋊C₄	—	86	1	no	—
292	C₂×C₂²⋊C₄	—	86	1	no	—
293	C₂×C₄²	—	43	2	no	—
294	C₂×C₄²	—	43	2	no	—
295	C₂×C₄²	—	43	2	no	—
296	C₂×C₄²	—	86	1	no	—
297	C₂×C₄²	—	86	1	no	—
298	C₂×C₄²	—	86	1	no	—
299	C₂×C₄²	—	86	1	no	—
300	C₂×C₄²	—	86	1	no	—
301	C₄⋊C₈	—	86	8	no	—
302	C₄×C₈	—	86	8	no	—
303	C₂⁴	#10621902	1	1	yes	characteristic
304	C₂²×C₄	—	86	8	no	—
305	C₂²×C₄	—	86	2	no	—
306	C₂²×C₄	—	86	2	no	—
307	C₂²×C₄	—	86	2	no	—
308	C₂²×C₄	—	86	2	no	—
309	C₂²×C₄	—	86	2	no	—
310	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
314	C₂²×C₄	#10621898	1	1	yes	characteristic
315	C₂²×C₄	#10621898	1	1	yes	characteristic
316	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
318	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
319	C₂²×C₄	#10621900	1	1	yes	characteristic
320	C₂²×C₄	#10621900	1	1	yes	characteristic
321	C₂²×C₄	#10621900	1	1	yes	characteristic
322	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	—	4	1	no	—
331	M₁₆	—	4	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	43	4	no	—
345	C₂×C₈	—	86	2	no	—
346	C₂×C₈	—	86	2	no	—
347	C₂×C₈	—	86	2	no	—
348	C₂×C₈	—	86	2	no	—
349	C₂×C₈	—	86	2	no	—
350	C₂×C₈	—	86	2	no	—
351	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	—
352	C₄⋊C₄	—	43	4	no	—
353	C₄⋊C₄	—	86	2	no	—
354	C₄⋊C₄	—	86	2	no	—
355	C₄⋊C₄	—	86	2	no	—
356	C₂²⋊C₄	—	86	2	no	—
357	C₂²⋊C₄	—	86	2	no	—
358	C₂²⋊C₄	—	172	1	no	—
359	C₂²⋊C₄	—	172	1	no	—
360	C₄²	—	43	4	no	—
361	C₄²	—	86	2	no	—
362	C₄²	—	86	2	no	—
363	C₄²	—	86	2	no	—
364	C₄²	—	86	2	no	—
365	C₄²	—	86	2	no	—
366	C₄²	—	172	1	no	—
367	C₄²	—	172	1	no	—
368	C₂³	—	2	4	no	—
369	C₂³	#13063283	1	1	yes	characteristic
370	C₂³	#13063287	1	1	yes	characteristic
371	C₂³	#13063287	1	1	yes	characteristic
372	C₂³	#13063301	1	1	yes	characteristic
373	C₂³	#13063310	1	1	yes	characteristic
374	C₂³	#13063316	1	1	yes	characteristic
375	C₂³	#13063320	1	1	yes	characteristic
376	C₂×C₄	—	86	8	no	—
377	C₂×C₄	—	86	8	no	—
378	C₂×C₄	—	86	8	no	—
379	C₂×C₄	—	86	4	no	—
380	C₂×C₄	—	86	4	no	—
381	C₂×C₄	—	172	2	no	—
382	C₂×C₄	—	172	4	no	—
383	C₂×C₄	—	172	4	no	—
384	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
385	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
386	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
387	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
388	C₂×C₄	#13063281	1	1	yes	characteristic
389	C₂×C₄	#13063282	1	1	yes	characteristic
390	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
391	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
392	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
393	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
394	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
395	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
396	C₂×C₄	#13063290	1	1	yes	characteristic
397	C₂×C₄	#13063290	1	1	yes	characteristic
398	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
399	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
400	C₂×C₄	#13063293	1	1	yes	characteristic
401	C₂×C₄	#13063296	1	1	yes	characteristic
402	C₂×C₄	#13063298	1	1	yes	characteristic
403	C₂×C₄	#13063302	1	1	yes	characteristic
404	C₂×C₄	#13063302	1	1	yes	characteristic
405	C₂×C₄	#13063303	1	1	yes	characteristic
406	C₂×C₄	#13063306	1	1	yes	characteristic
407	C₂×C₄	#13063307	1	1	yes	characteristic
408	C₂×C₄	#13063311	1	1	yes	characteristic
409	C₂×C₄	#13063315	1	1	yes	characteristic
410	C₂×C₄	#13063318	1	1	yes	characteristic
411	C₂×C₄	#13063324	1	1	yes	characteristic
412	C₈	—	2	4	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₈	—	86	4	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	#14582746	1	1	yes	characteristic
423	C₂²	#14582770	1	1	yes	characteristic
424	C₂²	#14582780	1	1	yes	characteristic
425	C₂²	#14582782	1	1	yes	characteristic
426	C₂²	#14582786	1	1	yes	characteristic
427	C₂²	#14582788	1	1	yes	characteristic
428	C₂²	#14582795	1	1	yes	characteristic
429	C₂²	#14583015	1	4	yes	—
430	C₄	—	86	8	no	—
431	C₄	—	344	2	no	—
432	C₄	—	172	4	no	—
433	C₄	#14582750	1	1	yes	characteristic
434	C₄	C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
435	C₄	#14582771	1	1	yes	characteristic
436	C₄	#14582775	1	1	yes	characteristic
437	C₄	#14582781	1	1	yes	characteristic
438	C₄	#14582787	1	1	yes	characteristic
439	C₄	#14582796	1	1	yes	characteristic
440	C₄	#14582803	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	#19132826	1	1	yes	characteristic
446	C₂	#19134431	1	2	yes	—
447	C₂	#19135297	1	2	yes	—
448	C₂	#19135341	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#341	C₂
socle	C₂³×C₄₃	C₄×D₄
prime radical	C₂⁴×C₄₃	#41
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#341	D₄₃
hypocenter	C₄₃	#10882
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#341

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
13. #14582927	C₄	semidirect
18. #14582662	C₄	semidirect
20. #14582660	C₄	semidirect
250. C₄₃	#10882	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#14582927	2
C₂²×C₈×Dic₄₃	2
#19134312	2
C₂×#14582660	2
#19134293	2
C₂×C₄₃×#341	2
#10882	43